1. Field of the Invention
The field of invention relates to both active and passive mass damper vibration control devices for reducing the vibrational response of a structure to an earthquake, wind, or the like.
2. Description of the Prior Art
A dynamic damper (hereinafter designated as a DD) may function as a vibration control device for a structure such as described, by way of example, in Japanese Pat. Laid-open No. 63-76932 and Japanese Pat. Publication No. 3-38386.
A prior art vibration model of a DD to be applied to a structure is also shown in FIG. 12 of the subject application, wherein m.sub.1 is the mass of the main body of the structure, comprising the main vibration system, and an additional mass body m.sub.d comprises the damping system. A spring constant of the main body of the structure is identified as k.sub.1. Masses m.sub.1 and m.sub.d are connected by a spring having a spring constant k.sub.d and a damper having a damping coefficient c.sub.d. Displacement of the structure mass m.sub.1 is indicated by the arrow x.sub.1, and displacement of the mass m.sub.d is indicated by the arrow x.sub.d.
A natural angular frequency of the main vibration system is given by: EQU .omega..sub.1 =(k.sub.1 /m.sub.1).sup.1/2
In the DD, a mass m.sub.d of tile damping system is designed so that the ratio of the mass m.sub.d to the mass.sub.1 of the main vibration system may be set to approximately become: EQU .mu.=m.sub.d /m.sub.1 .gtoreq.0.01
The natural angular frequency of the damping system is given by: EQU .omega..sub.d =(1/1+.mu.).omega..sub.1
A damping coefficient c.sub.d and a damping factor h.sub.d are represented by the following equations , respectively. EQU c.sub.d= 2 m.sub.d .omega..sub.d h.sub.d EQU h.sub.d =[3.mu./8(1+.mu.)]1/2
A prior art active mass damper (hereinafter AMD) used as an active type vibration control device is disclosed in U.S. Pat. No. 5,022,201.
FIG. 13 of the subject application shows a prior art vibration model of an AMD in which control force actuator means u(t), such as hydraulic power means or electromagnetic force means, is positioned between the main body of the structure having a mass m.sub.1 and the additional mass body having a mass m.sub.d to actively control the vibration of the structure.
In the AMP, assuming that the modulus of the spring between the main body of the structure and the additional mass body comprising the vibration control device is expressed by the equation EQU .omega..sub.d .ltoreq.(1/2).omega..sub.1
the control force u(t) is given by the following equation: EQU u(t)=G.sub.1 (dx.sub.1 /dt) G.sub.2 (dx.sub.d /dt)
wherein G.sub.1 is a gain in a circuit, including an automatic gain control circuit (AGC) or the like, against the response speed of the structure, and attains the correspondence of large inputs through small inputs (wherein G.sub.2 becomes a negative value). The second term in the above equation gives a damping property to the side of the additional mass body as well, and attains a stability thereof by adding the product of a gain G.sub.2 and a vibration speed on the side of the additional mass body to the control force.
There are some studies which try to add a spring having its spring constant k.sub.d to the AMD described above in parallel with the control force due to the actuator as shown in the vibration model of FIG. 14 and to obtain a vibration control effect to a certain degree with the control force of the AMD by means of less control force in comparison with that of an active tuned mass damper (hereinafter designated as ATMD).
In an ATMD, a spring constant k.sub.d is set so that the vibration of an additional mass body may synchronize with that of a structure, that is, EQU .omega..sub.d =.omega..sub.1
and the control force u(t) is, for example, given by the following equation: EQU u(t)=G.sub.1 (dx.sub.1 /dt)+G.sub.2 (dx.sub.d /dt)+G.sub.3 (x.sub.1 -x.sub.d)
wherein G.sub.3 is a gain having a negative sign and cancels a part of the inertial force applying on the additional mass body at a vibration time due to the third term in the above equation, so that the additional mass body may be vibrated by less control force.
Japanese Patent Publication No. 3-70075 discloses a vibration control device of an active type having a pattern for controlling the structural vibration due to an earthquake or the like by connecting a second additional mass body having a mass less than the additional mass body of the DD to the additional mass body of the DD through a spring and an actuator and by applying a control force on the second additional mass body from the actuator.
With reference to tile control direction of each prior art vibration control device described above, two kinds of systems can usually be considered depending on tile supporting method for an additional mass body to a structure:
(a) A system where only one vibration control device controls in all directions. PA1 (b) A system where one vibration control device controls in only one direction.
For example, an additional mass body is vibrated in all the directions within a horizontal plane and it is possible to maintain control in all directions by one vibration control device when the additional mass body is supported by a laminated rubber support, or a ball bearing, or is hung and supported by a universal joint or the like.
For example, in the case of connecting an additional mass body to a structure with a coil spring in a horizontal direction while supporting the additional mass body with a linear guide (straight rail or linear guide shaft or the like) or sliding the additional mass body along a circular track or in case of hanging and supporting the additional mass body with a hanger means, the vibation direction of the additional mass body is one-directional and only one-directional control is possible.
For the purpose of obtaining sufficient vibration control, however, the additional prior art mass body becomes very heavy and the problems increase.
One vibration control device can control in all directions, or, of course, a plurality of vibration control devices can be used. It is also possible to control in all directions with respect to a horizontal displacement by the combination of two-directional controls. In the case of (a) above, the advantage is that there is no waste with respect to the mass of the additional mass body. However, a mechanism for providing a control force and the control for the mechanism become complicated when applied to AMD or ATMD. In the case of (b) above, if it is desired to control in two directions within the horizontal plane of a structure, each vibration control device must be mounted separately in two directions. The additional mass body of the vibration control device in each separate direction does not function as a vibration control in a specific direction, and the vibration control device takes more space while the weight of total additional mass bodies increases in relation to the weight of the structure.
The present invention intends to solve the issues described above in the vibration control devices of the prior art. It is, accordingly, among the objects of the present invention to provide a vibration control device that can be operated by a minimal supply of energy and a minimal control force to effectively control the vibration of a structure against an earthquake, and which has a simple control mechanism wherein the weight of an additional mass body and the installation space for the device are minimized.